Problem: Simplify the following expression: $\sqrt{160} + \sqrt{250}$
Solution: First, try to factor any perfect squares out of the radicals. $= \sqrt{160} + \sqrt{250}$ $= \sqrt{16 \cdot 10} + \sqrt{25 \cdot 10}$ Separate the radicals and simplify. $= \sqrt{16} \cdot \sqrt{10} + \sqrt{25} \cdot \sqrt{10}$ $= 4\sqrt{10} + 5\sqrt{10}$ Finally, simplify by combining the terms. $= ( 4 + 5 )\sqrt{10} = 9\sqrt{10}$